Rotating Leaks in the Stadium Billiard

Abstract

The open stadium billiard has a survival probability, $P(t)$, that depends on the rate of escape of particles through the leak. It is known that the decay of $P(t)$ is exponential early in time while for long times the decay follows a power law. In this work we investigate an open stadium billiard in which the leak is free to rotate around the boundary of the stadium at a constant velocity, $\omega$. It is found that $P(t)$ is very sensitive to $\omega$. For certain $\omega$ values $P(t)$ is purely exponential while for other values the power law behaviour at long times persists. We identify three ranges of $\omega$ values corresponding to three different responses of $P(t)$. It is shown that these variations in $P(t)$ are due to the interaction of the moving leak with Marginally Unstable Periodic Orbits (MUPOs).

References in corpus (6)

• Leaking Chaotic Systems
• Open circular billiards and the Riemann hypothesis
• Peeping at chaos: Nondestructive monitoring of chaotic systems by measuring long-time escape rates
• Escape Rates Formulae and Metastability for Randomly perturbed maps
• Effect of noise in open chaotic billiards
• Influence of stability islands in the recurrence of particles in a static oval billiard with holes